1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 University of Puerto Rico4 University of Puerto Rico
We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.
Designs, Codes and Cryptography, 2014, Vol 70, Issue 1-2, p. 157-173